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A119948 Triangle of denominators in the square of the matrix with A[i,j] = 1/i for j <= i, 0 otherwise.

%I A119948 #13 Nov 06 2019 01:59:41
%S A119948 1,4,4,18,18,9,48,48,48,16,300,300,300,100,25,120,120,120,360,180,36,
%T A119948 980,980,980,2940,1470,294,49,2240,2240,2240,6720,6720,1344,448,64,
%U A119948 22680,22680,22680,22680,22680,4536
%N A119948 Triangle of denominators in the square of the matrix with A[i,j] = 1/i for j <= i, 0 otherwise.
%C A119948 The triangle of the corresponding numerators is A119947. The rationals appear in lowest terms.
%C A119948 The least common multiple (LCM) of row i gives [1, 4, 18, 48, 300, 360, 2940, 6720, 22680, ...], which coincides with A081528.
%F A119948 T(i,j) = denominator((A^2)[i,j]), where the lower triangular matrix A has elements a[i,j] = 1/i if j <= i, 0 if j > i.
%e A119948 The first rows of the table are:
%e A119948   [1];
%e A119948   [4, 4];
%e A119948   [18, 18, 9];
%e A119948   [48, 48, 48, 16];
%e A119948   [300, 300, 300, 100, 25];
%e A119948   [120, 120, 120, 360, 180, 36]; ...
%o A119948 (PARI) A119948_upto(n)={my(M=matrix(n, n, i, j, (j<=i)/i)^2); vector(n, r, apply(denominator, M[r, 1..r]))} \\ _M. F. Hasler_, Nov 05 2019
%Y A119948 Row sums give A119950. Row sums of the triangle of rationals always give 1.
%K A119948 nonn,easy,frac,tabl
%O A119948 1,2
%A A119948 _Wolfdieter Lang_, Jul 20 2006
%E A119948 Edited by _M. F. Hasler_, Nov 05 2019